Medium sudoku puzzles @ thesudoku.app

Sometimes after finding all of the hidden and naked singles, you will reach the point where you will still have cells with multiple candidates. At this step you will need to fill such cells with pencil marks.

Here come «naked pairs» and «naked triples» - basic solving techniques which will help you to eliminate some candidates and solve medium sudoku puzzles @ thesudoku.app.

Naked pairs

A «naked pair» is two cells, both in the same row, column or 3x3 unit, which have same two candidates left. It is clear that these candidates can be eliminated from any other cell in this row, column or 3x3 unit respectively.

Naked pair in 3x3 unit

Take a look at the highlighted unit. Cells G1 and I1, both have digits 3 and 8 - it is a naked pair. This means that after eliminating these digits from the cell H3 the only possible candidate for this cell will be 7.

Naked pair in 3x3 unit example
Figure 1. Naked pair in 3x3 unit
Solve puzzle from the Figure 1

Naked pair in a row

Take a look at the highlighted row E. Cells E2 and E9, both have digits 4 and 5 - it is a naked pair. This means that after eliminating these digits from the cell E8 the only possible candidate for this cell will be 1.

Naked pair in a row example
Figure 2. Naked pair in a row
Solve puzzle from the Figure 2

Naked pair in a column

Take a look at the highlighted column 3. Cells F3 and I3, both have digits 4 and 9 - it is a naked pair. This means that after eliminating these digits from the cell E3 the only possible candidate for this cell will be 9.

Naked pair in a row example
Figure 3. Naked pair in a column
Solve puzzle from the Figure 3

Naked triples

A «naked triple» is three cells from the same row, column or 3x3 unit, which have same three candidates left in different combinations. Since none of these candidates can be the solution in any other cell in this row, column or 3x3 unit, you can remove pencil marks from the other cells.

Naked triple in a row

Take a look at the highlighted row G. Cells G1, G2 and G3 share same digits 2, 3 and 6 - it is a naked triple. This means you can remove pencil mark 6 from the cell G4 and the only possible candidate for this cell will be 1.

Naked triple in a row example
Figure 4. Naked triple in a row
Solve puzzle from the Figure 4

Naked triple in a column

Take a look at the highlighted column 6. Cells B6, C6 and F6 share same digits 4, 7 and 9 - it is a naked triple. This means you can remove pencil mark 4 from the cell D6 and the only possible candidate for this cell will be 3.

Naked triple in a column example
Figure 5. Naked triple in a column
Solve puzzle from the Figure 5

Naked triple in 3x3 unit

Now take a look how removing pencil marks step by step will help you to solve the puzzle.

Take a look at the highlighted 3x3 unit. Cells H5, I5 and I6 share same digits 5, 8 and 9 - it is a naked triple. This means you can remove pencil mark 5 from the cell H4.

Now take a look at the highlighted column 4. After removing pencil mark 5 from the cell H4, this cell will share same digits 1 and 4 with the cell G4 - it is a naked pair in a column.

This means you can remove pencil mark 4 from the cell E4, so the only candidate for this cell will be 5.

Naked triple in 3x3 unit example
Figure 6. Naked triple in 3x3 unit
Solve puzzle from the Figure 6

Using «smart hint» feature @ thesudoku.app

Some combinations are not so easy to spot. Feeling stuck? Don't hesitate to use thesudoku.app «smart hint» feature. You can use this feature to get tips on all the basic solving techniques, including:

For example,aha with this hint you can easily remove pencil mark 3 from the cell C5.

Using smart hint feature example
Figure 7. Using smart hint
Solve puzzle from the Figure 7
ABCDEFGHI
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